Question

State A State B $52,245 $55,021 Sample mean Sample size Population standard Salary data from two random samples of high school teachers are shown to the right. Also shown are the population standard deviations. 44 49 $6,525 $6,877 deviation a. Construct a 95% confidence interval to estimate the difference in the average salaries of the high school teachers in these two states b. Based on the results in part a, can you conclude that a difference exists in the average salaries? a. Let population 1 the salaries of the high school teachers in State A and population 2 the salaries of the high school teachers in State B. The confidence interval is ($ (Round to the nearest dollar as needed.)

Answer 1

The statistical software output for this problem is:

Two sample Z summary confidence interval: 1 Mean of population 1 (Std. dev. = 6525) U2 Mean of population 2 (Std. dev. = 6877) 1- Difference between two means 95% confidence interval results: Difference n1 n2 Sample mean Std. err. L. limit U. limit 44 49 -2776 1390.2495 -5500.839 -51.161007

Hence,

a) 95% confidence interval will be:

($ -5501, $ -51)

b) Since the confidence interval only contain negative values and doesn't contain 0, we can conclude that difference exists.